diff --git a/sksurv/tree/tree.py b/sksurv/tree/tree.py
index aecc4a65..815e7387 100644
--- a/sksurv/tree/tree.py
+++ b/sksurv/tree/tree.py
@@ -206,7 +206,7 @@ def __init__(
 
     def __sklearn_tags__(self):
         tags = super().__sklearn_tags__()
-        tags.input_tags.allow_nan = self.splitter == "best"
+        tags.input_tags.allow_nan = self.splitter in ("best", "random")
         return tags
 
     def _support_missing_values(self, X):
diff --git a/tests/test_forest.py b/tests/test_forest.py
index a8cb74ef..ea482600 100644
--- a/tests/test_forest.py
+++ b/tests/test_forest.py
@@ -40,7 +40,10 @@ def test_fit_predict(make_whas500, forest_cls, expected_c):
     assert_cindex_almost_equal(whas500.y["fstat"], whas500.y["lenfol"], pred, expected_c)
 
 
-def test_fit_missing_values(make_whas500):
+@pytest.mark.parametrize(
+    "forest_cls,expected_cindex", [(ExtraSurvivalTrees, 0.7486232588273405), (RandomSurvivalForest, 0.7444120505344995)]
+)
+def test_fit_missing_values(make_whas500, forest_cls, expected_cindex):
     whas500 = make_whas500(to_numeric=True)
 
     rng = np.random.RandomState(42)
@@ -52,35 +55,18 @@ def test_fit_missing_values(make_whas500):
     X_train, y_train = X[:400], whas500.y[:400]
     X_test, y_test = X[400:], whas500.y[400:]
 
-    forest = RandomSurvivalForest(random_state=42)
+    forest = forest_cls(random_state=42)
     forest.fit(X_train, y_train)
 
     tags = forest.__sklearn_tags__()
     assert tags.input_tags.allow_nan
 
     cindex = forest.score(X_test, y_test)
-    assert cindex == pytest.approx(0.7444120505344995)
+    assert cindex == pytest.approx(expected_cindex)
 
 
-def test_fit_missing_values_not_supported(make_whas500):
-    whas500 = make_whas500(to_numeric=True)
-
-    rng = np.random.RandomState(42)
-    mask = rng.binomial(n=1, p=0.15, size=whas500.x.shape)
-    mask = mask.astype(bool)
-    X = whas500.x.copy()
-    X[mask] = np.nan
-
-    forest = ExtraSurvivalTrees(random_state=42)
-    with pytest.raises(ValueError, match="Input X contains NaN"):
-        forest.fit(X, whas500.y)
-
-    tags = forest.__sklearn_tags__()
-    assert not tags.input_tags.allow_nan
-
-
-@pytest.mark.parametrize("forst_cls,allows_nan", [(ExtraTreesClassifier, False), (RandomForestClassifier, True)])
-def test_sklearn_random_forest_tags(forst_cls, allows_nan):
+@pytest.mark.parametrize("forst_cls", [ExtraTreesClassifier, RandomForestClassifier])
+def test_sklearn_random_forest_tags(forst_cls):
     est = forst_cls()
 
     # https://scikit-learn.org/stable/developers/develop.html#estimator-tags
@@ -88,7 +74,7 @@ def test_sklearn_random_forest_tags(forst_cls, allows_nan):
     assert tags.target_tags.multi_output
     assert tags.requires_fit
     assert tags.target_tags.required
-    assert tags.input_tags.allow_nan is allows_nan
+    assert tags.input_tags.allow_nan
 
 
 @pytest.mark.parametrize("forest_cls", FORESTS)
diff --git a/tests/test_tree.py b/tests/test_tree.py
index 4178bfd1..fc2a214a 100644
--- a/tests/test_tree.py
+++ b/tests/test_tree.py
@@ -14,7 +14,7 @@
 from sksurv.compare import compare_survival
 from sksurv.datasets import load_breast_cancer, load_veterans_lung_cancer
 from sksurv.nonparametric import kaplan_meier_estimator, nelson_aalen_estimator
-from sksurv.tree import ExtraSurvivalTree, SurvivalTree
+from sksurv.tree import SurvivalTree
 from sksurv.util import Surv
 
 
@@ -837,19 +837,3 @@ def test_missing_values_best_splitter_to_right():
     # missing values go to the right
     y_expected = tree.tree_.value[4]
     assert_array_almost_equal(y_pred, y_expected)
-
-
-@pytest.mark.parametrize("is_sparse", [False, True])
-def test_missing_value_random_splitter_errors(is_sparse):
-    X = np.array([[3, 5, 7, 11, np.nan, 13, 17, np.nan, 19]], dtype=np.float32).T
-    y = Surv.from_arrays(
-        event=np.array([True, True, True, False, True, False, False, False, True]),
-        time=np.array([90, 80, 70, 60, 50, 40, 30, 20, 10]),
-    )
-
-    if is_sparse:
-        X = sparse.csr_matrix(X)
-
-    tree = ExtraSurvivalTree()
-    with pytest.raises(ValueError, match="Input X contains NaN"):
-        tree.fit(X, y)